numerical analysis of secondary motion of piston skirt in

Numerical Analysis of Secondary Motion of PistonSkirt in EnginesSunny NarayanMechanical Engineering Department, Qassim University, Saudi Arabia, 51431.

Vipul GuptaMechanical Engineering Department, Indus University, India, 174301.

(Received 4 May 2018; accepted 23 July 2018)

The motion of the piston pin plays an important role in the secondary motion of the skirt, and in the resultingnoise and vibration features of combustion engines. In the engine, the small gap between the piston skirt and thecylinder liner allows a small movement of the piston in a lateral direction, in addition to the reciprocating motionof the piston during operation of the engine. Although the piston is held in its cylinder bore by means of pistonrings, there is a small gap between the rings and the grooves, and hence it is free to move within this gap. Theexistence of the piston-liner gap puts a limit on the amplitude of piston motion, but not on the degree of freedomin the lateral, as well as the reciprocating, motion.

This work discusses a numerical model of the lateral motion of the skirt. Dynamic parameters of the skirt wereused to analyse this motion. Further, COMSOL-7 Multiphysics was used to simulate the motion of the skirt. Boththe simulation and the experiment showed a good correlation.

NOMENCLATURE

Fx Piston side-thrust forceω Angular velocityM Mechanical mobilitymp Dynamic mass of piston assemblymb Dynamic mass of engine blockIp Moment of inertia piston assemblyθ′′ Rotatory acceleration of piston assemblyθ′ Rotatory velocity of piston assemblyθ Tilting angle of pistonKp Dynamic stiffness of piston assemblyKb Dynamic stiffness of engine blockCp Dynamic damping coefficient of piston assemblyCb Dynamic damping coefficient of engine blockCC Dynamic contact damping coefficient of assemblyKC Dynamic contact stiffness of assemblyCθ Dynamic torsional damping coefficient of pistonKθ Dynamic torsional stiffness of pistonCCθ Dynamic torsional contact damping coefficient of

pistonKCθ Dynamic torsional contact stiffness of pistonX ′′p Piston assembly lateral accelerationX ′p Piston assembly lateral velocityXp Piston assembly lateral displacementX ′′b Block assembly lateral accelerationX ′b Block assembly lateral velocityXb Block lateral displacementMz Moment about piston pinXc Piston-liner gap

1. INTRODUCTION

Noise emissions from an internal combustion engine can beclassified as combustion-based noise, mechanical noise, aero-dynamic flow noise, etc. There is a small lateral gap betweenthe skirt and the liner due to manufacturing tolerances. Hence,the skirt is able to strike the liner in a lateral direction, in ad-dition to its usual reciprocating motion. This lateral motion ofthe skirt is also known as its slapping motion. Several numer-ical models have been studied in the past to analyse this sec-ondary motion of the skirt.1 These models have taken dynam-ics and tribological analysis into account. However, effects ofdamping have been neglected in past research works.2–5 Dur-ing analysis of lateral contact of the liner with the skirt, variousdynamic parameters need to be taken into account. Differentmethods to control the piston slapping motion includes opti-mization of skirt design parameters like piston pin offset, skirtstiffness, clearance size, and skirt profile. However, there is atrade-off between these parameters. As an example, reductionof the lateral gap between the skirt and the liner reduces thelateral motion of skirt, but at the same time, it increases fric-tional forces. Other alternative methods have been explored,including the use of dampers to reduce energy in the skirt-linersystem.6–8

The piston secondary motion is crucial to understand thevarious frictional forces in piston assembly, which contributeto 30–40% of total mechanical losses, and hence are a majorcause of inefficiency in an engine.9–11 The piston translatesfrom one side, to the liner, to the other side, due to the changein direction of the side-thrust force and due to the motion ofconnecting rod.12–15

The basic motion of the piston’s secondary motion can beseen in Fig. 1. A numerical model shown in Fig. 1 was used toanalyse this motion. The dynamic motion of the skirt may besummarized in matrix form as given by Eq. (1).1

International Journal of Acoustics and Vibration, Vol. 23, No. 4, 2018 (pp. 557–565) https://doi.org/10.20855/ijav.2018.23.41513 557

S. Narayan, et al.: NUMERICAL ANALYSIS OF SECONDARY MOTION OF PISTON SKIRT IN ENGINES

[mpiston

(1− bc

L

)+mpin

(1− ap

L

)mpiston

(bcL

)+mpin

(apL

)mpiston

(1− ap

L

)(bc − ap) +mpiston

(IpL

)mpiston

(apL

)(bc − ap)−mpiston

(IpL

)][e′′te′′b

]=[

Fh − (FIC + Fg + Ff ) tanφF−IC(ap − bc) + FgCp + FICCg +Mh +Mf

]. (1)

Figure 1. Basic model of piston secondary motion.1

2. BACKGROUND

The reciprocating primary motion of pistons in the model,which is determined by the pressure of combustion gas act-ing on top of the skirt, has been studied by McFadden et al.16

and Geng et al.17 Several simulations have been carried out tostudy the two-dimensional model of piston slap.18–20 Variousparameters considered include centre of gravity offset,21 skirtprofile,22 effects of variable inertial force,23 effects of frictionalforce,24 and effects of lubricating oil.25

McNally developed a numerical method to analyse pistonmotion, assuming that the skirt is a rigid body.26 Livanos etal. studied effects of friction on the piston motion of a marinediesel engine.27 The effects of engine speed and load wereanalysed and compared with empirical results. Mansouri et al.validated a numerical model of a skirt, considering the rough-ness and topology of the skirt.28 They developed various cor-relations and scaling laws that could be used for qualitativedesign of skirts. Lu et al. used the Jakobson-Floberg-Olsson(JFO) condition to study the rupture and reformation of an oilfilm.29 Gunelsu et al. used a Broyden’s scheme-based itera-tion phase method to analyse metal-to-metal contact forces.30

A spring-mass system connected by modal characteristics hasbeen sued to simulate the secondary motion of a skirt.31 Fanget al. studied the effects of machining surface grooves on pis-ton dynamics.32

Finite element analysis (FEA) is a versatile tool to study themechanical properties of materials. Mechanical behaviour ofbraided ropes using FEA is shown in Vu et al. and Gerdemeliet al.33, 34 This tool has been used to characterize the motionof skirts. Dursunkaya et al. introduced an elastohydrodynamicmodel of lubrication to simulate the motion of a skirt.35 Ther-mal deformations were calculated using an FEA model of askirt, in the case of a heavy truck diesel engine skirt. Radialdeformations were found to be dependent on engine load. Li etal. analysed the use of FEA to demonstrate the effects of vari-ations in inertia on piston motion and on the friction and lubri-cation behaviour between a piston skirt and a cylinder liner.36

Table 1. Engine specifications.

Component RatingBore 67 mm

Stroke 56 mmCompression ratio 4.5:1

Power 2.25 kW

Figure 2. Free body piston diagram.39

COMSOL 7 Multiphysics is one of the FEA packages thathave been widely used for modelling and simulation.37 Thestatic Hertz contact model for frictional forces has been ver-ified by using this software package.38 In the present study,this simulation tool was used to simulate the secondary motionof a KPKN2520 type single cylinder gasoline Kirloskar madeengine. Major features of this engine are presented in Table 1.

The novelty of the present work lies in the validation of theproposed model of the lateral motion of the skirt, with resultsobtained from a COMSOL simulation and the recorded blockvibration data. The proposed methodology needs further eval-uation, taking into account the influences of oil film lubrica-tion, motion of piston pins, and a selection of various materialsfor the designing of a skirt.

3. PISTON ASSEMBLY MODEL

3.1. Piston Side-Thrust Force (Fx)The existence of clearance between the skirt and cylinder

liner allows the piston to move and rotate freely within the con-fined region, resulting in the lateral motion of the skirt and slap.The main driving force is the side-thrust force imparted to theskirt by a connecting rod, as shown in Fig. 2. The skirt has thediameter Dp (mm) and length Hp (mm). The frictional forceacting between the rings and liner (Ffr), as well as betweenthe liner and skirt (Ff ). The contact force of the connectingrod with the skirt is resolved in horizontal (Frod,x) and verti-cal directions (Frod,y). Inertial forces are also resolved alongthe x-axis (FI,x), as well as the y-axis (FI,y). All forces areexpressed in N or kN.

The frictional forces between the piston skirt and cylinderliner, as well as between the rings and liner, act vertically along

558 International Journal of Acoustics and Vibration, Vol. 23, No. 4, 2018


the y-axis. The centre of mass of the piston assembly is at thehorizontal offset of Lx and at the vertical offset distance of Lyfrom the connecting rod position.

The force exerted by the connecting rod on the piston pincan be vertically decomposed along the x-axis, as well as they-axis. As the angle of the connecting rod changes as the pis-ton moves from bottom dead centre (BDC) to top dead centre(TDC), there will be a lateral force pushing the piston on tothe cylinder liner. The piston side-thrust force (Fx) takes intoconsideration both inertial forces as well as gas forces (Fg), asdeveloped by Guzzomi et al.,40 and is given by the followingequation, in terms of the crank radius-connecting rod lengthratio (K):

Fx =[Fg −mprω

2 (cos(θ) +K cos(2θ))]λ; (2)

where λ = K cos θ√1+[λ sin(θ)]2

,mp — mass of skirt (kg), θ — crank

angle (degree), r — crank radius (mm), ω — angular speed(rad/s).

3.2. Mobility Parameter DeterminationMechanical mobility (M ) is defined as the ratio of output ve-

locity of a structure to the excitation force acting on it. Mobil-ity between various input and output points is known as trans-fer mobility and mobility at a point is often called driving pointmobility. This parameter can be used to find the dynamic mass,stiffness, and damping constant of lumped parameter system.The point mobility M(jω) expresses the relation between re-sulting velocity response V (jω) and an exciting force F (jω),and is given as:39

M(jω) [m/N-s] =V (jω)

F (jω); (3)

M(jω) =−jω

((K −Mω2) + jCω

)Mω2(K + jCω)

. (4)

The mobility measurement was carried out to identify thedynamic properties of the piston and cylinder block. The re-sponse of the cylinder block was captured using an accelerom-eter mounted on the top of the engine block. The responseof the symmetric half portion piston skirt was measured us-ing COMSOL 7 FEA software for various cases. One suchsimulation is depicted in Fig. 3. Tetrahedral elements wereused to mesh the quarter part of the skirt. The materials usedfor this simulation were an aluminium alloy with a density of2700 kg/m3, Young’s modulus 72 GPa, and Poisson ratio of0.31.

Data inputs were fed to LABVIEW10 software for post pro-cessing. In order to ensure that the simulated results of the be-haviour of the piston’s secondary motion are comparable andcorrelated to the actual piston’s secondary motion, the mobil-ity was obtained using a running engine under various testingconditions. This was further used to determine the dynamicfeatures of the assembly.

Analysis of the frequency domain plots of mechanical mo-bility have shown that in the frequency range below the first

anti-resonance frequency(ωa =

√Km

), the point mobility

equation can be approximated as:39

M(jω) =−jmωa

. (5)

Figure 3. COMSOL Simulation.

Figure 4. Piston model.39

Above the anti-resonance frequency range, the point mobil-ity can be written as:39

M(jω) =−jωaK

. (6)

The above relations were used to find the dynamic mass andstiffness of the skirt, as well as liner system as shown later inTable 3. The interaction between the skirt and cylinder liner ofa piston assembly can be modelled as a three degree of freedomsystem, as shown in Fig. 4. The piston skirt is modelled as asingle point with a dynamic mass mp and moment of inertia(Ip) equal to the corresponding two degrees of freedom (Xp,θ). The cylinder block is modelled as a lumped system havinga dynamic mass mb with a single degree of freedom (Xb), asshown in matrix form in Eq. (2). The piston is located insidethe cylinder bore with a nominal clearance of 0.05 mm. Theclearance allows the piston to move in the lateral direction androtate about a piston pin. The clearance between the cylinderand liner Xc is modelled as a mechanical stop in the lateraldirection of piston motion with a hard stiffness.

The motion of the system is given by Eq. (7):39mp 0 00 mb 00 0 Ip

X ′′pX ′′bθ′′

+

Cp −Cp 0−Cp Cb + Cp 00 0 Cθ

X ′pX ′bθ′

+

Kp −Kp 0−Kp Kb +Kp 00 0 Kθ

Xp

Xb

θ

=

Fx0Mz

; (7)

International Journal of Acoustics and Vibration, Vol. 23, No. 4, 2018 559


Figure 5. Accelerometer locations.

Table 2. Testing conditions.

Case RPM Load1 2000 100%2 2000 80%3 3000 80%4 3000 100%5 3000 (motored)

wheremp — dynamic mass of skirt (kg), mb — dynamic massof block (kg), Ip — inertia of piston (kg-m2), Cp — dynamicdamping coefficient of skirt (N-s/m), Kp — dynamic stiffnesscoefficient of skirt (N/m), Cb — dynamic damping coefficientof block (N-s/m), Kb — dynamic stiffness coefficient of block(N/m), Fx — side-thrust force (N), Mz — net moment (N-m).

3.3. Experimental SetupThe block vibrations were measured by means of a Wilcox-

type mono-axial accelerometer, which was mounted in verti-cal (A) and horizontal orientations (B, C) on the engine block(Fig. 5). During the tests, engine speeds and loading conditionswere varied, as seen in Table 2.

4. RESULTS AND DISCUSSION

Figures 6 and 7 show the plot of the piston’s side-thrust forceat 2000 RPM and 3000 RPM conditions. Positive values offorce means contact towards thrust side of the skirt, whereasnegative values predict contact towards the anti-thrust side.Peak values were observed during the expansion stroke. Atzero values, the inertial forces acting on the skirt balance thegas forces on its top crown. As seen from these plots, side-thrust force changes its direction five times in a complete en-gine cycle, indicating instances of piston slapping contact asdepicted by circles.

COMSOL 7 software was then used to simulate piston sec-ondary motion, and hence compute the lateral piston velocityas shown in Figs. 8 and 9.

The lateral velocity of the skirt was seen in a range from−20to 20 m/s. It falls with an increase in engine loading values.Negative values of lateral velocity show clockwise tilting ofthe skirt, whereas the positive values predict an anti-clockwisetilt. Major changes were seen during suction and compressionstrokes. The velocity of piston approaches zero values nearthe top dead centre positions. Piston mobility was computedfor the given testing conditions, as depicted in Figs. 10 and11, from values of lateral velocity of the skirt obtained using aCOMSOL model (Figs. 8 and 9).

Figure 6. Representation of piston side-thrust force (2000 RPM).

Figure 7. Representation of piston side-thrust force (3000 RPM).

Figure 8. Representation of piston lateral velocity (2000 RPM).

Figure 9. Representation of piston lateral velocity (3000 RPM).



Figure 10. Representation of piston mobility (2000 RPM).

Figure 11. Representation of piston mobility (3000 RPM).

Figure 12. Representation of block velocity (2000 RPM).

Figure 13. Representation of block velocity (3000 RPM).

Figure 14. Representation of block mobility (2000 RPM).

Figure 15. Representation of block mobility (3000 RPM).

Similarly, mobility for the cylinder block was found(Figs. 14 and 15) using the numerical integration of the ac-celerometer data (in a vertical position), which gives valuesof the lateral block vibration velocity (Figs. 12 and 13). Lat-eral block velocities were found to be in range of −100 m/s to100 m/s, and were found to increase with engine speed.

Values of the first anti-resonant frequencies were found to beover 50 Hz. The curve for piston mobility had sharp and densepeaks, as compared to engine block mobility. This is becausethe skirt is in direct contact with intense gas forces, whereas theengine block acts as a nonlinear and time-dependent attenuatorfor these forces. Using the concept of anti-resonant frequencyas discussed in the previous sections, the various dynamic pa-rameters of a liner-piston system were computed for the giventest conditions. The results can be seen in Table 3.

The rotational motion of the skirt was simulated by solvingdynamic equations of motion and comparing with the resultsobtained from COMSOL as seen in Figs. 16–20. Both of thetrends showed a good correlation. The tilting of the skirt wasfound to be in the range of −0.2◦ to 0.2◦. Positive values oftilting angle means a tilt towards thrust side, whereas the neg-ative values imply a tilt towards anti-thrust side of the liner.Peak values of tilting were seen during the expansion and ex-haust strokes. As seen from the figures, the tilt angle of thepiston changes its direction at both dead centres. The pistonis predicted to slide for some duration before TDC along thecylinder liner. The piston’s tilt angle was seen to decrease withthe increase of load, as well as with speed.

Figures 21–25 show the simulated and measured vibratoryresponse of the cylinder block as captured by the accelerome-ter. The trends in the simulated vibration response of the cylin-der block show a good agreement with the measured vibrationresponse in ranges of 3–4 mm. In these figures, the impactof the piston on the cylinder wall results in a sudden increase



Table 3. Dynamic parameters of system.

Test Parameter ValueCase Piston Parameter Liner Parameter1 ωa = 65 Hz ωa = 67 Hz

[M(Jω)]ωa = [M(Jω)]ωa =2.5 ∗ 10−5 m/N-s 10−7 m/N-s

c = 109330 kg/s c = 42884 kg/sk = 1.63 ∗ 107 kg/s2 k = 4.2 ∗ 109 kg/s2

m = 63 kg m = 23754 kg2 ωa = 65 Hz ωa = 67 Hz

[M(Jω)]ωa = [M(Jω)]ωa =3.98 ∗ 10−5 m/N-s 10−7 m/N-s

c = 109330 kg/s c = 42884 kg/sk = 1 ∗ 107 kg/s2 k = 4.2 ∗ 109 kg/s2

m = 39 kg m = 23754 kg3 ωa = 100 Hz ωa = 63 Hz

[M(Jω)]ωa = [M(Jω)]ωa =3.1623 ∗ 10−5 m/N-s 1.99 ∗ 10−7 m/N-s


m = 50 kg m = 11937 kg4 ωa = 100 Hz ωa = 63 Hz



m = 63 kg m = 10105 kg5 ωa = 100 Hz ωa = 63 Hz



m = 83 kg m = 10105 kg

Figure 16. Representation of tilting motion (2000 RPM—80% load).

of the vibration amplitude and this is clearly marked in thediagram where a few impacts occurs. The induced vibrationamplitude of the cylinder block measured experimentally isslightly higher than the predicted induced vibration amplitude.This is due to several other contributing sources, like mechan-ical noises that add to the actual vibration data recorded.

The induced vibrations of the block increase with enginespeed, whereas the sliding duration falls with an increase invelocity. This is due to higher impact force and accelerationgenerated during the piston slap and a higher reaction impactforce from the liner. The effects of load and speed variations onpiston lateral motion are seen in Figs. 26 and 27. As the speedof engine increases, the side-thrust force, which is dependentupon speed, also increases. An increase in the magnitude of


Figure 18. Representation of tilting motion (3000 RPM—motored).

this side-thrust force acting on the piston results in the pistonbouncing off the liner more frequently for longer durations andthe sliding duration of the piston skirt along the liner falls. Atlow engine speeds, the vibration response of the cylinder blockinduced by the slapping contact of the piston has a longer du-ration till decay, as compared with higher engine speeds.

5. CONCLUSIONS

Noise emission from engines are the results of several con-tributing resources, out of which mechanical noise is a majorcontributor. Lateral motion of the skirt is a major contribu-tor in motion-based noise. There have been several numericalmodels that were proposed to study this motion. This workdiscusses one such two-dimensional modal model of pistonsecondary motion. Various dynamic parameters of the systemwere calculated using the concept of mobility. These parame-ters were used to generate profiles of piston secondary motion,resulting in block vibrations and the tilting angle of skirt. Theeffects of variations in various engine operational parameterswere also analysed. These calculated values were comparedwith simulated values obtained from the COMSOL 7 softwaretool, which validate the model. The sliding motion of the pis-ton along the liner was observed to increase, with an increasein load and speed, which is in agreement with the previous data





available.41 In future work, the lateral motion of skirt shouldalso takes into account the profile of the skirt, thermal defor-mations, and lubrication dynamics.

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Figure 23. Effect of engine speed on block vibrations (3000 RPM—motored).

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